CN114997028B - Time-saving random subspace method of space grid structure based on improved stable graph - Google Patents
Time-saving random subspace method of space grid structure based on improved stable graph Download PDFInfo
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Abstract
The invention relates to a time-saving random subspace method of a space grid structure based on an improved stable graph, which comprises the steps of firstly carrying out natural vibration characteristic analysis on the structure,obtaining modal parameters such as finite element analysis frequency, vibration mode and the like of the structure, then collecting vibration response signals of the structure under environmental excitation, constructing a generalized Hankel matrix by using the vibration response signals, and converting the projection of the Hankel matrix into the generalized Hankel matrixRAnd performing projection transformation of the matrix, performing weighted singular value decomposition on the projection matrix, setting a frequency search domain according to finite element analysis frequency, using modal confidence factors between the actually measured vibration modes of the measuring points and the finite element vibration modes as auxiliary stable axes, and comprehensively judging modal parameter identification results according to the frequency spectrum peak value, the stable graph and the auxiliary stable axes. The method is suitable for bridges, high-rise building structures and the like, is particularly suitable for modal parameter identification of large space grid structures with intensive modes, is high in calculation speed after improvement, and can effectively avoid modal omission.
Description
Technical Field
The invention relates to the technical field of modal parameter identification of structures, in particular to a time-saving random subspace method of a space grid structure based on an improved stable graph.
Background
With the rapid development of economy, large space structures such as stadiums, transportation hubs, landmark buildings and the like are largely built in China, such as ice ribbons, beijing great-rise international airports, national stadiums (bird nests), national swimming centers (water cubes) and the like. If engineering accidents happen to the large public building, not only can great property and life loss be caused, but also great social influence can be brought. Therefore, the health condition of the engineering structure is attracting more and more attention and attention. With the development of technologies such as structural modal parameter identification, damage identification and safety assessment and the rapid development of various sensors, testing equipment and the internet, a structural health monitoring system is laid for more and more important projects at home and abroad. Through monitoring the construction and operation stages of the structure, the stress, deformation and vibration conditions of the structure are obtained in time, the damage of the structure is found in time, the safety performance of the structure is evaluated, various early warnings can be made quickly, and corresponding reinforcement and maintenance measures can be provided, so that the method has very important significance.
Methods for assessing the health of a structure are based on both static and dynamic characteristics of the structure. The traditional static characteristic evaluation cannot accurately and comprehensively reflect the overall vibration characteristic of the structure, the environment of the engineering structure determines that the engineering structure must bear a large amount of dynamic load, and the vibration modal parameter of the structure is a main parameter for determining the dynamic characteristic of the structure and is also the core content of structural health monitoring.
The modal analysis theory combines some research ideas of structure dynamics, signal processing, mathematical statistics and system control, and gradually forms a set of unique theory. According to different modes of obtaining the structure modal parameters, modal analysis is divided into the following steps: firstly, a Finite Element technology is adopted, and a computer is utilized to carry out numerical value modal Analysis (FEA); second, experimental Modal Analysis (EMA) with known input and output responses; and thirdly, the method is developed on the basis of the EMA, and the Operation Modal Analysis (OMA) is identified only by using the output response of the structure in the operation state. OMA has the following advantages: (1) The vibration response data of the structure in the running state is only measured without exciting equipment; (2) The modal parameters identified by the method accord with actual working conditions and boundary conditions, additional mass is not generated in the detection process, and the real dynamic characteristics of the structure can be reflected; (3) The cost is low, the safety is good, the damage to the structure possibly caused by the excitation equipment can be avoided, and the normal use of the structure is not influenced.
Through the development of more than half a century, modal parameter identification has become an important branch in vibration engineering. After the 21 st century, OMA was rapidly developed and applied, and particularly in recent years, as modal parameter identification methods are increasingly applied to bridges, building structures and space structures, the original methods are continuously improved, and many new methods are introduced. The method mainly comprises a peak value method, a frequency domain decomposition method, a time sequence method, an ITD method, a characteristic system realization method, a random subspace method (SSI), wavelet transformation and the like.
The random subspace method under the environmental excitation comprises the following steps: the method is based on two random subspace methods of covariance drive (SSI-COV) and DATA drive (SSI-DATA). The theoretical basis of SSI-DATA is a state space equation of a time domain, and the SSI-DATA is widely applied due to the fact that the theory is perfect, and the recognition result is good. For example, chinese patent No. CN201110428858.4 discloses a transmission tower modal parameter identification method based on an improved subspace algorithm, which constructs a Hankel matrix by using a cross-power spectral function, and then performs weighted projection on the Hankel matrix, and a stable diagram is determined by using frequencies, damping ratios, and vibration mode tolerances at different orders. However, the number of columns of the Hankel matrix is assumed to be infinite, too much computer memory is consumed during QR decomposition of the Hankel matrix, the calculation efficiency is low, and particularly in analysis of a large-scale structure, the situation that the occupied memory is too large to analyze occurs, and the Hankel matrix is difficult to be used for online identification. In the identification process of the SSI-DATA method, the determination of the order of the system is the key of the method, and the order of the system is generally determined by using a stable graph. However, in the space grid structure, the number of stable points where the frequency, the damping ratio and the vibration mode tolerance meet the requirements is small, the stable axis is not obvious, and the position of the modal stable point cannot be determined.
Disclosure of Invention
In order to solve the problems, the invention provides a time-saving random subspace method based on a space grid structure of an improved stable graph, and the projection of a Hankel matrix is converted into the time-saving random subspace method based on the traditional random subspace methodRPerforming projection transformation on the matrix, and calculating modal parameters of the system; and then setting a frequency search domain, manufacturing an auxiliary stable axis, and comprehensively judging the position of the stable axis according to the frequency spectrum peak value, the stable graph and the auxiliary stable axis, so that the frequency, the damping ratio and the vibration mode of the structure can be accurately identified, the calculation efficiency is improved, and mode omission or misjudgment is avoided to a certain extent.
The invention is realized by the following steps:
a time-saving random subspace method of a spatial grid structure based on an improved stable graph comprises the following steps:
(1) Carrying out natural vibration characteristic analysis on the structure to obtain modal parameters of the structure, wherein the modal parameters comprise finite element analysis frequency and vibration mode;
(2) Arranging measuring points and collecting vibration response signals of the structure under environmental excitation;
(3) Constructing a generalized Hankel matrix by using the vibration response signal of the structure;
(4) Converting the projection transformation of the Hankel matrix into the projection transformation of the R matrix after QR decomposition, and performing weighted singular value decomposition on the projection matrix;
(5) Setting a frequency search domain according to finite element analysis frequency, obtaining actual measurement modal parameters of the structure by using singular value decomposition results, and drawing a stable graph;
(6) Carrying out spectrum analysis on the vibration response signal to obtain a spectrogram of the structure;
(7) Calculating modal confidence factors between the actually measured vibration modes and the finite element vibration modes of the measuring points to serve as auxiliary stabilizing axes;
(8) And comprehensively judging the modal parameters of the identification structure according to the position of the peak value of the spectrogram, the stable graph and the auxiliary stable axis.
Preferably, in the step (1), the structural model is imported into a numerical analysis software, and the structural model is subjected to natural vibration characteristic analysis according to structural design data to obtain modal parameters of the structure. By the method, the self-vibration characteristic analysis is carried out according to the structural design data, and more accurate and more fit-with-engineering actual modal parameters can be obtained.
Preferably, in the step (2), the sensors are arranged according to the actual conditions of the engineering and the characteristics of the structural vibration mode, and the acquired vibration response signals are acceleration, speed or displacement response signals according to the difference of the sensors. By the method, proper measuring points and reference points are selected and arranged, and the sensors are arranged according to the structural vibration mode characteristics, so that relatively complete structural information can be obtained from the limited number of measuring points.
Preferably, step (3) includes: and preprocessing the vibration response signal of the structure, and constructing a generalized Hankel matrix by using the preprocessed vibration response signal.
Preferably, the preprocessing includes filtering, smoothing, and eliminating trend terms. By the method, the noise influence of the vibration response signal can be reduced through pretreatment.
Preferably, in step (4), hankel matrix is subjected toYQR decomposition is carried out to obtain an orthogonal matrixQAnd is provided withTriangular matrixRWill beRThe matrix is divided into the pastR p And the futureR f Two parts are as follows:
transforming the projection transformation of Hankel matrix intoRProjective transformation of the matrix:
to projection matrixO i Performing weighted singular value decomposition, and defining weighting matrix by CVA methodW 1 AndW 2 ：
in the formula (I), the compound is shown in the specification,Iis a matrix of the unit, and is,U 1 、S 1 、V 1 respectively an orthogonal matrix, a singular value matrix and an orthogonal matrix obtained by weighted singular value decomposition. By the method, the projection transformation of the Hankel matrix is converted into the projection transformation of the R matrix, then the projection matrix is subjected to weighted singular value decomposition, and the modal parameters of the system are calculated, so that the calculation of a high-dimensional matrix can be effectively avoided, and the calculation efficiency is improved.
Preferably, in the step (5), assuming that the model has different orders, a plurality of modal parameters of different orders are obtained, including frequency, damping ratio and mode shape, and frequency, damping ratio and mode shape tolerance are set, and a stable point meeting the tolerance is drawn on the stable graph.
Preferably, the method only performs the stability map determination on the modal parameters in the search frequency domain, specifically:
the frequency tolerance in the stability plot is the percentage of difference between the calculated frequencies of the orders:
the damping ratio tolerance in the stability diagram is the percentage of the difference between the damping ratios of the orders:
the mode tolerance in the stability plot is the percentage difference in MAC value between orders of mode deviation 1:
frequency, damping ratio and mode tolerance
、
、
The closer to 0 the value of (d) is, the more stable it is. By the method, the frequency search domain is set, and only the modal parameters in the domain are judged by the stable graph, so that the calculation time is greatly shortened.
Preferably, in step (6), when performing the spectrum analysis, the sampling frequency of the structure is input, and an appropriate fourier transform calculation length and a window function are selected for calculation.
Preferably, in step (7), according to the correlation between the actual measurement mode and the finite element mode, the finite element mode of the system is introduced into the stability diagram, an auxiliary mode tolerance is set, the MAC value between the actual measurement mode and the finite element mode of each measurement point is calculated, the point meeting the tolerance is taken as an auxiliary stability axis, and the point is taken as an auxiliary judgment basis of the stability diagram, so as to judge the true and false mode modes. By the method, modal omission and misjudgment can be effectively avoided.
Compared with the prior art, the invention has the beneficial effects that: the time-saving random subspace method based on the space grid structure of the improved stable graph, which is provided by the invention, has the following specific beneficial effects:
(1) After the projection transformation of the Hankel matrix is converted into QR decompositionRPerforming projection transformation on the matrix, and then performing weighted singular value decomposition on the projection matrix to further calculate modal parameters of the system, so that a high-dimensional matrix is prevented from being calculated, and the calculation efficiency is improved;
(2) In the process of drawing the stable graph, a frequency search domain is set according to a theoretical frequency analysis result, only modal parameters in the search frequency domain are subjected to stable graph judgment, and the reduction of calculation efficiency caused by overhigh sampling frequency is avoided;
(3) According to the correlation between the actually measured vibration mode and the finite element vibration mode, the finite element vibration mode of the system is introduced into the stability diagram, an auxiliary stability axis is obtained by calculating the MAC value between the actually measured vibration mode and the finite element vibration mode of each measuring point, the auxiliary stability axis is used as an auxiliary judgment basis of the stability diagram, and finally the position of the stability axis is comprehensively judged according to the frequency spectrum peak value, the stability diagram and the auxiliary stability axis, so that the frequency, the damping ratio and the vibration mode of the structure can be accurately identified, and mode omission or misjudgment is avoided to a certain extent.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It should be apparent that the drawings in the following description are merely exemplary, and that other embodiments can be derived from the drawings provided by those of ordinary skill in the art without inventive effort.
The structures, ratios, sizes, and the like shown in the present specification are only used for matching with the contents disclosed in the specification, so that those skilled in the art can understand and read the present invention, and do not limit the conditions for implementing the present invention, so that the present invention has no technical significance, and any structural modifications, changes in the ratio relationship, or adjustments of the sizes, without affecting the functions and purposes of the present invention, shall fall within the scope covered by the technical contents disclosed in the present invention.
FIG. 1 illustrates a flow chart of a preferred embodiment of the present invention;
FIG. 2 is a schematic view illustrating a model of a grid structure;
FIG. 3 is a diagram illustrating a site layout in accordance with a preferred embodiment of the present invention;
FIG. 4 is a graph illustrating a time course before and after filtering at a certain measuring point;
fig. 5 exemplarily shows a conventional stabilization chart;
FIG. 6 illustrates an improved stabilization chart of a preferred embodiment of the present invention;
fig. 7 (a) to 7 (l) exemplarily show comparison graphs of the theoretical mode shape and the calculated mode shape recognition result of the order 1~6 of a certain grid structure.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the present invention is further described in detail below with reference to the embodiments and the accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
In the description of the present invention, the terms "comprises/comprising," "consists of … …," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a product, apparatus, process, or method that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such product, apparatus, process, or method if desired. Without further limitation, an element defined by the phrases "comprising/including … …", "consisting of … …" does not exclude the presence of additional like elements in a product, apparatus, process or method that includes the element.
It is to be understood that, unless otherwise expressly specified or limited, the terms "disposed," "mounted," "connected," "secured," and the like are intended to be inclusive and mean, for example, that any suitable arrangement may be utilized and that any suitable connection, whether permanent or removable, or integral, may be utilized; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
It will be further understood that the terms "upper," "lower," "front," "rear," "left," "right," "top," "bottom," "inner," "outer," "center," and the like are used in an orientation or positional relationship illustrated in the drawings for convenience in describing and simplifying the invention, and do not indicate or imply that the device, component, or structure being referred to must have a particular orientation, be constructed in a particular orientation, or be operated in a particular manner, and should not be construed as limiting the invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or to implicitly indicate the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
The following describes the implementation of the present invention in detail with reference to preferred embodiments.
FIG. 1 is a flow chart of a time-saving random subspace method of a spatial grid structure based on an improved stability graph according to an embodiment of the present invention. Exemplary embodiments of the present invention will be described in detail below with reference to specific drawings.
The spatial grid structure mentioned in the present invention may be a square quadrangular pyramid grid structure, or other spatial grid structures are obviously applicable.
(1) According to the structural design data, carrying out natural vibration characteristic analysis on the structure to obtain modal parameters of the structure, including finite element analysis frequency and vibration mode;
in one embodiment, software such as Midas, SAP2000 and ANSYS is used for natural vibration characteristic analysis, and a structure model is imported during analysis to obtain the theoretical frequency and the vibration mode of the structure.
(2) Measuring points are distributed, and vibration response signals of the structure under environmental excitation are acquired;
because the space structure has too many nodes, the vibration response signals of all the nodes cannot be measured or are not suitable to be measured, in one embodiment, according to the actual condition of engineering and the characteristics of the structure vibration mode, peak values of the vibration modes of all orders are selected as measuring points, in addition, a plurality of reference points are arranged in the middle of the structure, sensors are arranged, and the acquired vibration response signals can be acceleration, speed or displacement response signals according to the difference of the sensors.
For the sensor arrangement, the arrangement of each structure is different and can be arranged at the upper chord node and the lower chord node of the grid structure, but in large-scale practical engineering, a berm (capable of getting on people) is arranged near the lower chord of the grid structure, purlins and roof are arranged at the upper chord, and the purlins and the roof cannot get on people and can only be arranged at the lower chord nodes.
(3) Constructing a generalized Hankel matrix by using the vibration response signal of the structure;
in one embodiment, the vibration response signals of the structure are preprocessed, and the preprocessed vibration response signals are used for constructing a generalized Hankel matrix.
Preferably, the preprocessing includes filtering, smoothing, eliminating trend terms, etc., to reduce the noise contribution of the vibration response signal.
(4) After the projection transformation of the Hankel matrix is converted into QR decompositionRPerforming projection transformation of the matrix, and performing weighted singular value decomposition on the projection matrix;
in one embodiment, the orthogonal matrix obtained by QR decomposition of the Hankel matrixQAnd lower triangular matrixRIs eliminated in the identification process, and is lower triangular matrixRThe singular values obtained by SVD are the same as those obtained by Hankel matrix, so it will beRMatrix division into the pastR p And the futureR f Two parts are as follows:
transforming the projective transformation of the Hankel matrix intoRProjective transformation of the matrix:
to projection matrixO i Performing weighted singular value decomposition, and defining weighting matrix by CVA methodW 1 AndW 2 ：
in the formula (I), the compound is shown in the specification,Iis a matrix of the units,U 1 、S 1 、V 1 respectively an orthogonal matrix, a singular value matrix and an orthogonal matrix obtained by weighted singular value decomposition. By means of orthogonal matricesU 1 Sum singular value matrixS 1 And obtaining modal parameters of the system.
(5) Setting a frequency search domain according to the obtained finite element analysis frequency, obtaining actual measurement modal parameters of the structure by using singular value decomposition results, and drawing a stable graph;
in one embodiment, the stability map is obtained by assuming that the model has different orders, obtaining a plurality of modal parameters of different orders, including frequency, damping ratio and mode shape, setting frequency, damping ratio and mode shape tolerance, comparing the modal parameters of different orders, and drawing the stability points meeting the tolerance on the stability map. For most structures, only the first few orders of the structure are considered, and the rear most parts are unnecessary parts, and the parts consume a large amount of time in the process of drawing the stability graph, so that before the stability graph judgment, a frequency search domain is given first, and the stability graph judgment is carried out on the modal parameters in the region, so that the calculation time is greatly reduced.
The frequency tolerance in the stability plot is the percentage of difference between the calculated frequencies of the orders:
the damping ratio tolerance in the stability diagram is the percentage of the difference between the damping ratios of the orders:
the mode tolerance in the stability plot is the percentage difference in MAC value between orders of mode deviation 1:
frequency, damping ratio and vibration mode tolerance
、
、
The closer to 0 the value of (d) is, the more stable it is.
(6) Carrying out spectrum analysis on the vibration response signal to obtain a spectrogram of the structure;
in one embodiment, the spectral analysis first needs to calculate a power spectral density function, then performs singular value decomposition on the power spectral density function, and decomposes the power spectral density function into a set of self-power spectrums of the single-degree-of-freedom system, where the frequency corresponding to the peak of each power spectral curve is the characteristic frequency of the system. The power spectral density function needs to input the sampling frequency of the structure during calculation, and a proper Fourier transform calculation length and a window function are selected.
(7) Calculating modal confidence factors between the actually measured vibration modes and the finite element vibration modes of the measuring points to serve as auxiliary stabilizing axes;
in one embodiment, the auxiliary mode shape tolerance is specifically set, and the point where the tolerance is met is taken as the auxiliary stability axis.
More specifically, the tolerance between the measured vibration modes of different orders meets the requirement, which only indicates the relative stability of the vibration modes and cannot indicate the relationship between the vibration modes and the finite element vibration modes. In many practical projects, many auxiliary structures are omitted during finite element analysis, so that the actually measured frequency value is greater than the finite element analysis frequency, but the vibration modes of the two have greater correlation, therefore, the finite element vibration mode of the system is introduced into a stability diagram, an auxiliary vibration mode tolerance is set, the MAC value between the actually measured vibration mode and the finite element vibration mode is calculated, the point meeting the tolerance is taken as an auxiliary stability axis, and the point is taken as an auxiliary judgment basis of the stability diagram, so that the true and false modal vibration modes are judged.
(8) And comprehensively judging the modal parameters of the identification structure according to the position of the peak value of the spectrogram, the stable graph and the auxiliary stable axis.
In one embodiment, the peak value of the spectrogram, the stable axis in the stable graph and the auxiliary stable axis all correspond to modal parameters of each order, and the problems of near-frequency overlapping and modal density exist in a large-span spatial grid structure, and all the order modes of the structure cannot be identified from one of the near-frequency overlapping and modal density, so that the three are comprehensively considered in the step, and the frequency, damping ratio, vibration mode and other modal parameters of the identified structure are comprehensively judged by combining the three.
Example of engineering application:
the finite element analysis frequency and the vibration mode of the structure were obtained by analyzing the natural vibration characteristics of the square pyramid lattice structure shown in fig. 2 by Midas. From fig. 7 (a) to 7 (l) the vibration modes of finite element analysis show that the vibration mode of the first 6 orders of the structure is vertical integral vibration, according to the vibration mode characteristics of the structure, the peak point of each vibration mode is selected as a measuring point at the lower chord node of the net rack, and a plurality of reference points are arranged in the middle of the structure, and the measuring point arrangement diagram is as shown in fig. 3. And applying 30s of white noise which is not related to each other in three directions of each measuring point, and then performing time interval analysis and calculation, wherein the sampling frequency is 100Hz, and obtaining the vertical displacement response of all the measuring points.
The displacement response signal of the structure is filtered, and the time course curve before and after filtering at a certain measuring point is shown in fig. 4.
According to the Midas analysis result, the order of the stable graph in the example is 10-30 orders, the frequency domain search domain is set to be 5-23Hz, the calculation length of Fourier transform in the frequency spectrum analysis is 512, a Hanning window is selected as a window function, the tolerance of frequency is set to be 5%, the tolerance of a damping ratio is set to be 20% (because the calculation error of the damping ratio is large, the tolerance of the damping ratio is properly widened), the tolerance of a vibration mode is set to be 10%, the tolerance of an auxiliary vibration mode is set to be 10%, the traditional stable graph and the improved stable graph are respectively shown in fig. 5 and 6, the frequency identification result is shown in table 1, the damping ratio identification result is shown in table 2, and the theoretical vibration mode and the actually measured calculated vibration mode result are shown in fig. 7 (a) to fig. 7 (l).
TABLE 1 net rack model frequency identification results
TABLE 2 net rack model damping ratio identification result
In fig. 6, "+" indicates an axis of auxiliary stabilization between the measured mode shape and the finite element mode shape, (-) indicates a point where the frequency, the damping ratio, and the mode shape are stabilized, "diamondindicates a point where the frequency and the damping ratio are stabilized, and". Smallcircle "indicates a point where the frequency and the mode shape are stabilized. The time length is 30s, the number of sampling points is 3000, the traditional SSI-DATA calculation time is 29.077s, the calculation time of the method is 3.752s, and the calculation efficiency is greatly improved.
In addition, the spatial structure has many rods and complex modal information, and as can be seen from fig. 5, the number of points (x) where the frequency, the damping ratio and the mode shape are stable is too small, and some points are not on one stable axis, and the modal order and the position of the stable axis cannot be judged from the stable diagram alone. As can be seen from fig. 6, a false frequency phenomenon exists at the position of the 1 st order mode, the overlapping frequency can be removed according to the auxiliary stabilizing axis, the 4 th order and the 5 th order frequencies are covered by the 6 th order signal peak bandwidth region, the mode energy is small, the spectrogram cannot be identified, the positions of the 4 th order and the 5 th order modes can be judged by using the stabilizing map and the auxiliary stabilizing axis, and the mode omission can be effectively avoided. As can be seen from tables 1 and 2, the maximum error of the frequency identification by the SSI-DATA method is 2.737%, the damping ratios of the other orders are greater than the limit value 20% except the damping ratio of the first order, wherein the error of the damping ratio of the 6 th order is 142.8%, and the error can be directly eliminated if the error is too large. The maximum error of the frequency identification of the improved method is improved to 0.787%, the maximum error of the damping ratio identification is improved to 22%, and the identification accuracy of the frequency and the damping ratio is greatly improved. As can be seen from FIGS. 7 (a) to 7 (l), the actually measured vibration mode is substantially consistent with the vibration mode of the finite element analysis, and therefore, the method has a great engineering application value.
It will be readily appreciated by those skilled in the art that the above-described preferred embodiments may be freely combined, superimposed, without conflict.
The above description is intended to be illustrative of the preferred embodiment of the present invention and should not be taken as limiting the invention, but rather, the invention is intended to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (8)
1. A time-saving random subspace method of a spatial grid structure based on an improved stable graph is characterized by comprising the following steps:
(1) Performing natural vibration characteristic analysis on the structure to obtain modal parameters of the structure, including finite element analysis frequency and vibration mode;
(2) Arranging measuring points and collecting vibration response signals of the structure under environmental excitation;
(3) Constructing a generalized Hankel matrix by using the vibration response signal of the structure;
(4) Converting the projection transformation of the Hankel matrix into the projection transformation of the R matrix after QR decomposition, and performing weighted singular value decomposition on the projection matrix;
(5) Setting a frequency search domain according to finite element analysis frequency, obtaining actual measurement modal parameters of the structure by using singular value decomposition results, and drawing a stable graph; the method comprises the steps of obtaining a plurality of modal parameters of different orders, including frequency, damping ratio and vibration mode, assuming that a model has different orders, setting the tolerance of the frequency, the damping ratio and the vibration mode, and drawing stable points meeting the tolerance on a stable graph;
(6) Carrying out spectrum analysis on the vibration response signal to obtain a spectrogram of the structure;
(7) Calculating modal confidence factors between the actually measured vibration modes and the finite element vibration modes of the measuring points to serve as auxiliary stabilizing axes; introducing the finite element mode shape of the system into a stable graph according to the correlation between the actually measured mode shape and the finite element mode shape, setting an auxiliary mode shape tolerance, calculating an MAC value between the actually measured mode shape and the finite element mode shape of each measuring point, taking a point meeting the tolerance as an auxiliary stable axis, and taking the point as an auxiliary judgment basis of the stable graph so as to judge the true and false mode shape;
(8) And comprehensively judging the modal parameters of the identification structure according to the position of the peak value of the spectrogram, the stable graph and the auxiliary stable axis.
2. The method according to claim 1, wherein in the step (1), the structural model is imported into a numerical analysis software, and the structural model is subjected to natural vibration characteristic analysis according to structural design data to obtain modal parameters of the structure.
3. The method as claimed in claim 1, wherein in the step (2), the sensors are arranged according to the actual conditions of the engineering and the structural mode characteristics, and the acquired vibration response signals are acceleration, velocity or displacement response signals according to the difference of the sensors.
4. The method of claim 1, wherein step (3) comprises: and preprocessing the vibration response signal of the structure, and constructing a generalized Hankel matrix by using the preprocessed vibration response signal.
5. The method of claim 4, wherein preprocessing comprises filtering, smoothing, and removing trend terms.
6. The method of claim 1, wherein in step (4), the Hankel matrix is processedYQR decomposition is carried out to obtain an orthogonal matrixQAnd lower triangular matrixRWill beRMatrix division into the pastR p And the futureR f Two parts are as follows:
transforming the projective transformation of the Hankel matrix intoRProjective transformation of the matrix:
to projection matrixO i Performing weighted singular value decomposition, and defining weighting matrix by CVA methodW 1 AndW 2 ：
in the formula (I), the compound is shown in the specification,Iis a matrix of the units,U 1 、S 1 、V 1 respectively an orthogonal matrix, a singular value matrix and an orthogonal matrix obtained by weighted singular value decomposition.
7. The method according to claim 1, wherein the stability map determination is performed only on modal parameters in the search frequency domain, specifically:
the frequency tolerance in the stability plot is the percentage of difference between the calculated frequencies of the orders:
the damping ratio tolerance in the stability diagram is the percentage of the difference between the damping ratios of the orders:
the mode tolerance in the stability plot is the percentage difference in MAC value between orders of mode deviation 1:
frequency, damping ratio and mode tolerance
、
、
The closer to 0 the value of (d) is, the more stable it is.
8. The method of claim 1, wherein in step (6), when performing the spectral analysis, the sampling frequency of the structure is input, and an appropriate fourier transform calculation length and window function are selected for calculation.
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